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Modified HSS iteration methods for a class of complex symmetric linear systems

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Abstract

In this paper, we introduce and analyze a modification of the Hermitian and skew-Hermitian splitting iteration method for solving a broad class of complex symmetric linear systems. We show that the modified Hermitian and skew-Hermitian splitting (MHSS) iteration method is unconditionally convergent. Each iteration of this method requires the solution of two linear systems with real symmetric positive definite coefficient matrices. These two systems can be solved inexactly. We consider acceleration of the MHSS iteration by Krylov subspace methods. Numerical experiments on a few model problems are used to illustrate the performance of the new method.

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Authors and Affiliations

  1. School of Mathematics and Computer Science, Guizhou Normal University, 550001, Guiyang, People’s Republic of China

    Zhong-Zhi Bai

  2. State Key Laboratory of Scientific/Engineering Computing, Institute of Computational Mathematics and Scientific/Engineering Computing, Academy of Mathematics and Systems Science, Chinese Academy of Sciences, P.O. Box 2719, 100190, Beijing, People’s Republic of China

    Zhong-Zhi Bai

  3. Department of Mathematics and Computer Science, Emory University, Atlanta, GA, 30322, USA

    Michele Benzi

  4. Department of Mathematical Sciences, Xi’an Jiaotong University, 710049, Xi’an, People’s Republic of China

    Fang Chen

  5. Department of Mathematics and Physics, Xi’an University of Post and Telecommunication, 710121, Xi’an, People’s Republic of China

    Fang Chen

Authors
  1. Zhong-Zhi Bai
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  2. Michele Benzi
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  3. Fang Chen
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Corresponding author

Correspondence to Zhong-Zhi Bai.

Additional information

Communicated by C.C. Douglas.

This work was supported by The National Basic Research Program (No. 2005CB321702) and The National Outstanding Young Scientist Foundation (No. 10525102), P. R. China, and by The US National Science Foundation grants DMS-0511336 and DMS-0810862.

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Bai, ZZ., Benzi, M. & Chen, F. Modified HSS iteration methods for a class of complex symmetric linear systems. Computing 87, 93–111 (2010). https://doi.org/10.1007/s00607-010-0077-0

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  • DOI: https://doi.org/10.1007/s00607-010-0077-0

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